Vertex algebras associated with elliptic affine Lie algebras

TL;DR

This paper explores the connection between elliptic affine Lie algebras and vertex $ ext{C}((z))$-algebras, constructing related Lie algebra families and establishing a framework for their modules.

Contribution

It introduces a novel association between elliptic affine Lie algebras and vertex $ ext{C}((z))$-algebras, expanding the understanding of their structure and representations.

Findings

Constructed two families of Lie algebras related to elliptic affine Lie algebras

Established a category of modules for these vertex algebras

Provided a new framework linking elliptic affine Lie algebras with vertex algebra theory

Abstract

We associate elliptic affine Lie algebras with what are called vertex $\C((z))$-algebras and their modules in a certain category. In the course, we construct two families of Lie algebras closely related to elliptic affine Lie algebras.